The commutativity degree of semigroup of order p^α q^β
Subject Areas : Statistics
Mehrdad
Azadi
1
(Mathematics Department, Central Tehran Branch, Islamic Azad University, Tehran, Iran.)
mandana
ghaneei
2
(Mathematics Department, Central Tehran Branch, Islamic Azad University, Tehran,Iran.)
Keywords: مرکز ساز, رده هم ارزی, درجه جابجایی, نمایش متناهی نیم گروه ها,
Abstract :
T‎he commutativity‎ degree of a finite non-commutative semigroup S is defined to be the probability‎ of choosing a pair (x,y) of the elements of S such that x commutes with y‎. Obviously if S is a abelian semigroup, then commutativity degree of S is 1. In this study, we consider semigroups are non-commutative and finite. ‎For a given positive integer n=p^α q^β where p and q are primes (2≤p
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